41. CONFERENCES, SUMMER SCHOOLS, TALKS, WORKSHOPS [1] Eindhoven 23 FOR PARTICIPATION 7 Amsterdam (The Netherlands) 1426 September 1998 arend heytingCentenary PROGRAM heyting Lectures, heyting Symposium, Thematic Day 8 http://colibri.let.uu.nl/html/html.24-1998/general.html

CONFERENCES, SUMMER SCHOOLS, TALKS, WORKSHOPS Eindhoven 23 June 1998 ZIC Colloquium on Logic and Theoretical Computer Science dr. ir. Hans de Nivelle: "Implementation of a resolution theorem prover" Montpellier (France) 10-12 August 1998 ICCS'98 6th International Conference on Conceptual Structures CALL FOR PARTICIPATION Saarbruecken (Germany) 14-16 August 1998 FHCG-98 Joint Conference on Formal Grammar, Head-driven Phrase Structure Grammar and Categorial Grammar PROGRAM Saarbruecken (Germany) 14-16 August 1998 FHCG-98 Joint Conference on Formal Grammar, Head-driven Phrase Structure Grammar and Categorial Grammar PROGRAM Melbourne (Australia) 28 August 1998 ACM-SIGIR'98 Post-Conference Workshop on "Multimedia Indexing and Retrieval" EXTENDED Deadline: 19 June 1998 Freiburg (Germany) 7-9 September 1998 LD'98 The First International Workshop on Labelled Deduction http://www.informatik.uni-freiburg.de/~ld98 CALL FOR PARTICIPATION Amsterdam (The Netherlands) 14-26 September 1998 Arend Heyting Centenary PROGRAM: Heyting Lectures, Heyting Symposium, Thematic Day

42. HISTOIRE DE LA LOGIQUE- LA LOGIQUE MATHÉMATIQUE Translate this page preuve ou de justification jouent un rôle fondamental. arend heyting(1898-1980). On développera donc dans les années 1930 une http://logique.uqam.8m.com/histoire10.htm

Free Web site hosting - Freeservers.com Web Hosting - GlobalServers.com Choose an ISP NetZero High Speed Internet ... Dial up $14.95 or NetZero Internet Service $9.95 LA LOGIQUE MATHÉMATIQUE Suite au courant fondationnel, soutenu surtout par Frege et Russell, la logique s’intéresse d’une part à une approche sémantique (dans l’esprit de la théorie des modèles) et d’autre part à une entreprise de formulation d’une théorie de la démonstration, amorcée par le programme de Hilbert. Ce programme cherche à fournir une preuve absolue de la cohérence de l’arithmétique, considérant que les preuves de cohérence des mathématiques n’étaient jusque là que relatives et fondées uniquement sur l’arithmétique, qui elle-même ne pouvait être ramenée à la cohérence d’une autre théorie plus fondamentale. David Hilbert (1862-1943) Hilbert propose son programme lors du Congrès International de Mathématiques de Paris en 1900. La première solution qui est présentée (1904) consiste en une preuve syntaxique, par laquelle on prouve directement qu’il est impossible de déduire un énoncé et sa négation à partir des axiomes d’une théorie. Cette preuve ne s’intéresse pas à la sémantique, mais seulement aux symboles mathématiques et logiques. Dans la mesure où l’on vérifie que c’est bien le cas de tous les énoncés par récurrence (inductivement), la preuve est circulaire et insuffisante. Pour répondre à cette critique, Hilbert fait la distinction entre le principe mathématique de récurrence et la méthode intuitive de raisonnement par récurrence, ce qui ne fut pas suffisant.

43. Full Alphabetical Index Translate this page 355) Herschel, Caroline (188*) Herschel, John (143*) Herstein, Israel (295*) Hesse,Ludwig (165*) Heuraet, Hendrik van (170) heyting, arend (62*) Hilbert http://www.geocities.com/Heartland/Plains/4142/matematici.html

44. AL Seminar (1994) Franchella () Abstract This talk presents the contentof the unpublished notes that the Dutch mathematician arend heyting wrote in http://www.jaist.ac.jp/is/labs/ono-ishihara-lab/ono-lab/ALseminars/al-seminars94

AL seminar (1994) (5) February 16, 1994 Title: $B9`=q49$(%7%9%F%`$N%b%8%e%i@-(B Speaker: Yoshihito Toyama (JAIST) Abstract: $BFs$D$N9`=q49$(%7%9%F%`$,%A%c! OB%7%9%F(B $B%`$b%A%c! ZL@$5$l$F$$$k!#$3$N%b%8%e(B $B%i@-$O!"9`=q49$(%7%9%F%`$N@~7A@-$d=E$J$j$NM-L5$J$I$N9=B$$K$O$$$C$5$$L54X78(B $B$K>o$K@.N)$9$k$?$a!"J#;($J9=B$$r$b$D9`=q49$(%7%9%F%`$KBP$9$k$-$o$a$F6/NO$J(B $B2r@O R2p$7$?$$!#(B (6) March 11, 1994 Title: Normal Proofs and Their Grammar Speaker: Masako H. Takahashi (Tokyo Institute of Technology) Abstract: (7) March 18, 1994 Title: Monad as Modality Speaker: Satoshi Kobayashi (Ryukoku University) Abstract: ZL@$+$i%b%J%I$K4p$E$/(B imperative $B$J4X?t7?%W%m%0%i%`$rF3$/$3$H(B $B$,$G$-$k!#(B (8)-1 April 1, 1994 Title: Relational and partial variable sets and basic predicate logic Speaker: Silvio Ghilardi ($B%_%i%NBg3X?t3X2J(B) Abstract: The content of this talk is a joint work by S. Ghilardi and G. Meloni, extending to intuitionistic-like semantics some previous investigations concerning modal and temporal logic. The proposed semantics is the following: keep possible worlds to be a category, but in correspondence to arrows require a relation between the domains. The method for analyzing this semantics is Lawvere's doctrinal approach. It turns out that a sound and complete axiomatization is obtained simply by dropping the so-called Frobenius and Beck-Chevalley conditions in first order logic. (8)-2 April 1, 1994

45. Moviecity - Nederlands Grootste Aktuele Filmdatabase. heyting Scriptfragmenten uit originele werkscripten van Hetty heyting - Fotogalerij- Rekwistietenoverzicht meteen trammelant met Onkel X. En arend Vogel is http://www.moviecity.nl/?page=dvd&ID=2805

46. [Phil-logic] Re:Intuitionism-Heyting Vollstandigkeit der Principia ist die Vollstandigkeit meines Systems ME in der bestmoglichen Weise gesichert. , quoted in AS Troelstra, arend heyting and His http://philo.at/pipermail/phil-logic/2001-September/000031.html

[Phil-logic] Re:Intuitionism-Heyting Graham Solomon gsolomon@wlu.ca Wed, 26 Sep 2001 12:48:37 -0400 (EDT) Previous message: [Phil-logic] Re:Intuitionism-Heyting Next message: [Phil-logic] Re:Intuitionism-Heyting Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] axioms, and deleted those which he thought are nonconstructive. That is hardly possible. Hilbert-Ackermann would seem a more likely source of inspiration. Yes, I likely misremembered the story. Previous message: [Phil-logic] Re:Intuitionism-Heyting Next message: [Phil-logic] Re:Intuitionism-Heyting Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]

47. Full Alphabetical Index Translate this page 2275) Herschel, Caroline (1760*) Herschel, John (2821*) Herstein, Yitz (295*) Hesse,Otto (165*) Heuraet, Hendrik van (170) heyting, arend (62*) Higman, Graham http://alas.matf.bg.ac.yu/~mm97106/math/alphalist.htm

Full Alphabetical Index The number of words in the biography is given in brackets. A * indicates that there is a portrait. A Abbe , Ernst (602*) Abel , Niels Henrik (2899*) Abraham bar Hiyya (641) Abraham, Max Abu Kamil Shuja (1012) Abu Jafar Abu'l-Wafa al-Buzjani (1115) Ackermann , Wilhelm (205) Adams, John Couch Adams, J Frank Adelard of Bath (1008) Adler , August (114) Adrain , Robert (79*) Adrianus , Romanus (419) Aepinus , Franz (124) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (313*) Aitken , Alec (825*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (12)

48. File 22-1-95.TXT Dateilänge 46 KB * * * * Bearbeiter N. EGBERT JAN(003) 9 BETH,EVERT WILLEM(003) 9 heyting,arend(003) 9 http://www.phil.uni-passau.de/dlwg/ws03/22-1-95.txt

ERLÄUTERUNGEN ZU DEN LITERATURHINWEISEN: 1. FORMALBIBLIOGRAPHISCHE INFORMATIONEN V - Verfasser TI - Titel (hinter "..." evtl. ein Abstract) Z - Zeitschriften-(Festschrift usw.) Titel BD - Band (mögliche Abkürzungen: "S" f. Sonderheft, "J" f. Jahrbuch JG - Jahrgang SE - Seiten DT - Dokumententyp (mögliche Abkürzung: "JO" f. Zeitschrift, "CO" f. Kongressakte, "HO" f. Festschrft, "RE" f. Reader SPR - Sprache des Artikels (mögliche Abkürzungen: die ersten vier Buchstaben der englischen Bezeichnung der Sprache, also z.B. "GERM" für deutsch). 2. INHALTLICHE INFORMATION Eine inhaltliche Erschliessung der Nachweise wurde erreicht durch 1. eine Anzahl dem Text entnommener Sachwörter oder Namen (als sogenannte "Deskriptoren"), 2. die Kennzeichnung des thematischen Zusammenhangs der Deskriptoren, 3. die Angabe der Wichtigkeit der Deskriptoren im vorliegenden Dokument In (035)/Kant, Immanuel (020)/Lorentz, Hendrik Antoon (035) SPR: GERM (freie Naturgesetz (035)/Erfahrung (035)/Deskript.) Relativitätstheorie

49. IPM - Homepage direct proofs. In 1930, Brouwer s student arend heyting gave thefirst axiomatization of intuitionistic logic. Kripke semantics http://www.ipm.ac.ir/IPM/activities/ViewProgramInfo.jsp?PTID=206

50. Neue Seite 1 Translate this page van Heuraet, Hendrik (1633 - 1660). heyting, arend (1898 - 1980). Hilbert,David (23.1.1862 - 14.2.1943). Hill, George William (1838 - 1914). http://www.mathe-ecke.de/mathematiker.htm

Abbe, Ernst (1840 - 1909) Abel, Niels Henrik (5.8.1802 - 6.4.1829) Abraham bar Hiyya (1070 - 1130) Abraham, Max (1875 - 1922) Abu Kamil, Shuja (um 850 - um 930) Abu'l-Wafa al'Buzjani (940 - 998) Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843) Aepinus, Franz Ulrich Theodosius (13.12.1724 - 10.8.1802) Agnesi, Maria (1718 - 1799) Ahlfors, Lars (1907 - 1996) Ahmed ibn Yusuf (835 - 912) Ahmes (um 1680 - um 1620 v. Chr.) Aida Yasuaki (1747 - 1817) Aiken, Howard Hathaway (1900 - 1973) Airy, George Biddell (27.7.1801 - 2.1.1892) Aithoff, David (1854 - 1934) Aitken, Alexander (1895 - 1967) Ajima, Chokuyen (1732 - 1798) Akhiezer, Naum Il'ich (1901 - 1980) al'Battani, Abu Allah (um 850 - 929) al'Biruni, Abu Arrayhan (973 - 1048) al'Chaijami (? - 1123) al'Haitam, Abu Ali (965 - 1039) al'Kashi, Ghiyath (1390 - 1450) al'Khwarizmi, Abu Abd-Allah ibn Musa (um 790 - um 850) Albanese, Giacomo (1890 - 1948) Albert von Sachsen (1316 - 8.7.1390)

51. Spreads And Choice In Constructive Mathematics 1 BISHOP, ERRETT AND DOUGLAS BRIDGES, Constructive analysis, SpringerVerlag1980. 2 heyting, arend, Intuitionism, an introduction, North-Holland 1956. http://www.math.fau.edu/Richman/docs/spreads.htm

Spreads and choice in constructive mathematics Fred Richman Florida Atlantic University Boca Raton, FL 33431 21 June 2001 Abstract An approach to choice-free mathematics using spreads: If constructing a point satisfying property P requires choice, replace this problem by that of constructing a nonempty set of elements satisfying P . Then construct a spread, without choice, whose elements satisfy P . The theory is developed and several examples are given. Constructing points without choice There are many situations in (constructive) mathematics where you want to construct a point, say a real or complex number, with certain characteristics. The three problems I want to consider are constructing a complex number that satisfies a given nonconstant polynomial over the complex numbers-the fundamental theorem of algebra constructing a point in a given set of positive measure, and constructing a point in the intersection of a given countable family of open dense subsets of a complete metric space-the Baire category theorem. For each of these problems, the traditional solutions appeal to countable choice, or rather to the stronger

52. The Ascending Tree Condition condition, Bull. Amer. Math. Soc. 49 (1943), 225236. 3 heyting, arend,Intuitionism, an introduction, North-Holland 1956. 4 JACOBSSON http://www.math.fau.edu/Richman/docs/new-acc.htm

The ascending tree condition Fred Richman Florida Atlantic University 23 December 2001 Abstract. A strengthening of the ascending chain condition allows a choice-free constructive development of the theory of Noetherian modules. Related topics in the theory of PID's and elementary divisor rings are also explored. The theory of finitely generated modules over a Noetherian ring admits a satisfactory constructive development by considering finitely presented modules over a coherent Noetherian ring [5]. From a classical point of view, every finitely generated module over a Noetherian ring is finitely presented-in particular, every Noetherian ring is coherent-so this also provides an adequate classical theory. From a constructive point of view, being finitely presented, rather than finitely generated, is a stronger property that must be assumed even if the ring is a field. The definition of Noetherian used in [5] was the ascending chain condition on finitely generated ideals, in the form If I I I is a chain of finitely generated ideals, then there exists

53. Luitzen Egbertus Jan Brouwer Brouwer s principal students were Maurits Belinfante and arend heyting; thelatter, in turn, was the teacher of Anne Troelstra and Dirk van Dalen. http://plato.stanford.edu/entries/brouwer/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change MAR Luitzen Egbertus Jan Brouwer In classical mathematics, he founded modern topology by establishing, for example, the topological invariance of dimension and the fixpoint theorem. He also gave the first correct definition of dimension. In philosophy, his brainchild is intuitionism, a revisionist foundation of mathematics. Intuitionism views mathematics as a free activity of the mind, independent of any language or Platonic realm of objects, and therefore bases mathematics on a philosophy of mind. The implications are twofold. First, it leads to a form of constructive mathematics, in which large parts of classical mathematics are rejected. Second, the reliance on a philosophy of mind introduces features that are absent from classical mathematics as well as from other forms of constructive mathematics: unlike those, intuitionistic mathematics is not a proper part of classical mathematics. The Person Chronology Brief Characterization of Brouwer's Intuitionism Brouwer's Development of Intuitionism ... Related Entries The Person Brouwer studied at the (municipal) University of Amsterdam where his most important teachers were Diederik Korteweg (of the Korteweg-de Vries equation) and, especially philosophically, Gerrit Mannoury. Brouwer's principal students were Maurits Belinfante and Arend Heyting; the latter, in turn, was the teacher of Anne Troelstra and Dirk van Dalen. Brouwer's classes were also attended by Max Euwe, the later world chess champion, who published a game-theoretical paper on chess from the intuitionistic point of view (Euwe, 1929), and who would much later deliver Brouwer's funeral speech. Among Brouwer's assistants were Heyting, Hans Freudenthal, Karl Menger, and Witold Hurewicz, the latter two of whom were not intuitionistically inclined. The most influential supporter of Brouwer's intuitionism outside the Netherlands at the time was, for a number of years, Hermann Weyl.

54. Er Uendelighed Aktuel Eller Potentiel? På den anden side er der intuitionisterne, som i denne opgave repræsenteresaf LEJ.Brouwer (18811966) og arend heyting (1898-1980). http://www.filosofi.net/Afhandlinger/Html/uendelighed.htm

Uendelighed, aktuel eller potentiel? er et BA-projekt ved: Center for Filosofi, Filosofisk Institut Odense Universitet, Syddansk Universitet Af Lisbeth Jørgensen lisbeth_jorgensen@yahoo.com Vejleder: Cynthia M. Grund Forside: Georg Cantor og L.E.J.Brouwer set med uendelighedens brilleglas Afleveret d. 8/1 2001 Indholdsfortegnelse Problemformulering Indledning Uendelighedens paradokser Baggrundshistorien for distinktionen mellem aktuel og potentiel uendelighed ... Litteraturliste Problemformulering Er uendelighed aktuel eller potentiel? Hvad er argumenterne for at uendelighed er aktuel henholdsvis potentiel? Hvilke nye problemer udløser disse argumenter? Indledning Hvad er uendelighed? Findes uendelighed, er der noget uendeligt i verden? Eller er uendelighed bare noget vi bruger som begreb, en slags grænse som egentlig ikke er der. I det overordnede spørgsmål om hvad uendelighed er, ligger også en undersøgelse af tid og rum, men jeg vil i denne opgave begrænse mig til den matematiske uendelighed. Således hører denne opgave ind under matematikkens filosofi. Min filosofiske indgangsvinkel til dette emne er at tage udgangspunkt i de paradokser der opstår ved nærmere betragtning af uendelighed. Man kan så spørge hvilken opfattelse af uendelighed der har betydning for at de forskellige paradokser opstår. Kan de forskellige forklaringer af matematisk uendelighed give en løsning på paradokserne, uden at nye opstår? Uendelighed optræder i matematikken bl.a. i mængdelære og i geometri. Mængden af naturlige tal er uendelig stor; uanset hvor langt man tæller, er det altid muligt at tælle én til. Der er således ikke noget største naturligt tal – enhver kandidat til et sådant kan med det samme blive større ved at lægge én til. I geometriens studie af rummet kan en linje deles uendeligt mange gange, og ethvert interval kan blive underinddelt i flere underinddelinger. Den tanke at en proces kan fortsættes i det uendelige, introducerer uendelighed som potentiel; uendelighed er aldrig noget der kan nås. I vores standard aritmetik (tallære) opfattes uendelighed på den anden side også som aktuel: Mængden af naturlige tal opfattes som

55. Learning-Org Jul 2000: Systematical Patterns In Boolean Logic L However, eventually one of his students (arend heyting) managed to createa model for this intuitionistic, constructivist logic of Brouwer. http://www.learning-org.com/00.07/0052.html

Systematical Patterns in Boolean Logic LO25063 [complex] From: AM de Lange ( amdelange@gold.up.ac.za Date: Next message: KiWiDressler: "Systems Thinking.. or Not? LO25064" Previous message: AM de Lange: "pow-wa-ha LO25062" In reply to: AM de Lange: "Efficiency and Emergence LO25047 [complex]" Next in thread: Gavin Ritz: "Efficiency and Emergence LO25044 [complex]" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Mail actions: [ respond to this message ] [ mail a new topic ] Replying to LO25047 Dear Organleaners, Greetings to you all. In my reply to the topic Efficiency and Emergence LO25047, I did somethings so as to initiate this contribution. I wrote: >philospher CS Peirce as "inclusive denials". .... It is often >called among logicians as Peirce's "dagger" and can be (snip) >This "dagger" seems to be a self-destruction of truth in statements. This "handle" gives me the opportunity to say something more on the relationship between logic and Learning Organisations. I specifically avoid calling this contribution "Systems Thinking and

56. Learning-Org May 1999: "Junk" Science LO21531 In the mean while one of Brouwer s students arend heyting created a logical systemto generate the intuitionistic theorems which Brouwer so painstakedly had http://www.learning-org.com/99.05/0074.html

"Junk" Science LO21531 AM de Lange ( amdelange@gold.up.ac.za Fri, 7 May 1999 10:16:31 +0200 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: W.M. Deijmann: "Buildings, Offices as LO enabler LO21532" Previous message: Philip Pogson: "Buildings, Offices as LO enabler LO21530" In reply to: John Gunkler: ""Junk" Science LO21521" Next in thread: Nick Arnett: "Category Theory LO21542 -was "Junk" Science" Reply: Nick Arnett: "Category Theory LO21542 -was "Junk" Science" Reply: Winfried Dressler: ""Junk" Science LO21569" Reply: Winfried Dressler: ""Junk" Science LO21570" Reply to [ author only ] [ Learning-Org list ] Replying to LO21521 Dear Organlearners, jgunkler@sprintmail.com Greetings John, Thank you very much for explaining in more detail what you meant. When you warned against fallicious thinking, I had the uneasy feeling that you were using the shot gun with the sawn off barrel, spraying hail all over the place, hoping to hit someone's thoughts. Now I know that you had something much more clear in mind. Just two points on the name of the topic. If we are going to stay on

57. What Do Types Mean? In arend heyting, editor, Constructivity in Mathematics, pages 101128. Inarend heyting, editor, Constructivity in Mathematics, pages 81-100. http://portal.acm.org/citation.cfm?id=766967&dl=ACM&coll=portal&CFID=11111111&CF

58. Finitism Now jump to arend heyting and Abraham Robinson in the 20th century. The latter wasthe genius at Yale responsible for most of modern aerodynamic wing theory. http://www.ccir.ed.ac.uk/~jad/vantil-list/archive-Sep-2000/msg00030.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index Finitism To : "The Van Til List" < vantil-list@XC.Org Subject : Finitism From : "David Hewins" < dave_hewins@onebox.com Date : Sat, 09 Sep 2000 09:48:25 -0500 List-Unsubscribe mailto:leave-vantil-list-230528T@XC.Org Reply-To : "The Van Til List" < vantil-list@XC.Org Prev by Date: Logic Resources wordmp3.com Next by Date: Reconciliation! Prev by thread: Logic Resources wordmp3.com Next by thread: Reconciliation! Index(es): Date Thread

59. Diccionario De Autores Translate this page (1889-1971). HEYDE, JOHANNES ERICH (nac. 1892). HEYMANS, GERARDUS (1857-1930).heyting, arend (nac. 1898). HIEROCLES DE ALEJANDRÍA fl. 420. HIEROCLES EL ESTOICO http://cibernous.com/colabora/comunes/diccionario.htm

DICCIONARIO DE AUTORES A B C D ... Z A AALL, ANATHON ABBAGNANO, NICOLA (nac. 1901) ABBT, THOMA ABELARDO (PEDRO) ABENALARIF ABENALSID ABENARABI ABENHAZAM ABENMASARRA ABENTOFAIL ABU SALT ACHILLUNI, ALESSANDRO ACKERMANN, WILHELM ACONCIO, GIACOMO [ACONZIO, CONCIO; ACONTIUS, JACOBUS] entre 1492-1520-ca. 1568 ADAMSON, ROBERT (fallecido 1181) ADELARDO DE BATH (fl. 1100) ADICKES, ERICH ADLER, ALFRED ADLER, MAX ADORNO, THEODOR W[IESENGRUND] AECIO fl. ca. 150 AGRIPPA DE NETTESHEIM, HEINRICH CORNELIUS [HENRICUS CORNELIUS] AHRENS, HEINRICH AJDUKIEWICZ, KAZIMIERZ ALANO DE LILLE (ca. 1128-1202) ALBERINI, CORIANO ALBERT, HANS (nac. 1921) ALBERTO (SAN) ALBINO fl. 180 ALBO, JOSEF [YOSEF] ca. 1380-ca. 1444 ALEJANDRO DE AFRODISIA ALEJANDRO DE HALES (ca. 1185-1245) fl. ca. 300 ALEMBERT, JEAN LE ROND D' ALEXANDER, SAMUEL ALFARABI ALGAZELLI (ALGAZEL) ALIOTTA, ANTONIO ALKINDI ALONSO DE LA VERACRUZ (nac. 1906) ALTHUSSER, LOUIS (nac. 1918) (fallecido 1206/7) AMBROSIO (SAN) ca. 340-397 AMELIO fl. 240 AMMNOIO HERMEIOU [AMMNONIO DE HERMIA] fl. 530

60. Geert Willems Kaptein 0211-1950 te Arnhem. arend overleed op 12-01-1944 te Arnhem. Kinderen 09-09-1895te Apeldoorn, (zoon van Gerrit van LOHUYZEN en Johanna Geertruida heyting). http://home.wanadoo.nl/kappetein/derden/4724.htm

De nakomelingen van Geert Willems Kaptein, Hoogeveen vanaf 1800 Opgesteld door Claudia van ´t Veer Geert Willems KAPTEIN Hij trouwde Albertje Roelofs DODEVIS Geert overleed op 27-12-1829 te Hoogeveen. Kinderen: i Roelof KAPTEIN ii Arend Geerts KAPTEIN iii Willem Geerts KAPTIJN Tweede Generatie Roelof KAPTEIN Hij trouwde Alberdina ENTING , (dochter van Berend ENTING en Geesje SIKKENS ) overl. 21-11-1856 te Hoogeveen. Roelof overleed op 29-08-1865 te Hoogeveen. Kinderen: i Geert KAPTEIN , geb. 2 aug 1827 te Hoogeveen, overl. 23-07-1849 te Zwartsluis. ii Berend KAPTEIN , geb. 2 feb 1829 te Zwolle, overl. 27-08-1830 te Hoogeveen. iii Berend KAPTEIN , geb. 29-06-1831 te Hoogeveen, overl. 13-03-1837 te Hoogeveen. iv Albert KAPTEIN geb. 3 nov 1834. v Berend KAPTEIN geb. 21-04-1839. Arend Geerts KAPTEIN Hij trouwde (1) Jacoba Roelofs BOUWMEESTER , getrouwd 04-06-1826 te Hoogeveen, (dochter van Roelof Jans BOUWMEESTER en Albertje Alberts KLINKIEN ). Hij trouwde (2) Catharina MAATJES , getrouwd 17-11-1855 te Hoogeveen, geb. 9 aug 1826 te Hoogeveen, (dochter van Derk Geerts MAATJES en Klaasje Alberts METSELAAR ). Arend overleed op 20-03-1887 te Hoogeveen.

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