Attributes, sets, partial sets and identity

P. C. Gilmore

Compositio Mathematica (1968)

  • Volume: 20, page 53-69
  • ISSN: 0010-437X

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Gilmore, P. C.. "Attributes, sets, partial sets and identity." Compositio Mathematica 20 (1968): 53-69. <http://eudml.org/doc/88985>.

@article{Gilmore1968,
author = {Gilmore, P. C.},
journal = {Compositio Mathematica},
keywords = {set theory},
language = {eng},
pages = {53-69},
publisher = {Wolters-Noordhoff Publishing},
title = {Attributes, sets, partial sets and identity},
url = {http://eudml.org/doc/88985},
volume = {20},
year = {1968},
}

TY - JOUR
AU - Gilmore, P. C.
TI - Attributes, sets, partial sets and identity
JO - Compositio Mathematica
PY - 1968
PB - Wolters-Noordhoff Publishing
VL - 20
SP - 53
EP - 69
LA - eng
KW - set theory
UR - http://eudml.org/doc/88985
ER -

References

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  2. Willard Van Orman Quine [2] Mathematical Logic, Harvard University Press, Cambridge, revised edition, 1951. Zbl0579.03001MR45661
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  4. Willard Van Orman Quine [4] Word and Object, The Technology Press of MIT and John Wiley and Sons, Inc., New.York and London, 1960. Zbl0093.00915MR111674
  5. Willard Van Orman Quine [5] Set Theory and Its Logic, The Belknap Press of Harvard University Press, Cambridge, 1963. Zbl0122.24601MR274272
  6. Abraham A. Fraenkel [6] Abstract Set Theory, North-Holland Publishing Co., Amsterdam, 1953. Zbl0050.04903MR56660
  7. Alonzo Church [7] "A formulation of the simple theory of types", Journal of Symbolic Logic, Vol. 5 (1940), 56-68. Zbl0023.28901MR1931
  8. Thoralf Skolem [8] "Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre" , Conférences au 5e. Congrès [1922] des Mathématiciens Scandinaves (Helsingfors, 1923) 218-232. Zbl49.0138.02JFM49.0138.02
  9. R.O. Gandy [9] "On the axiom of extensionality - Part I", Journal of Symbolic Logic, Vol. 21 (1956) 36-48. Zbl0073.00801MR75899
  10. R.O. Gandy [10] "On the axiom of extensionality - Part II", Journal of Symbolic Logic, Vol. 24 (1959) 287-300. Zbl0097.24601MR136548
  11. Kurt Gödel [11] The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory, Princeton University Press, Princeton, 1940; second printing, 1951. Zbl0061.00902MR2514
  12. Dana Scott [12] "Lectures on Boolean-valued models for set theory", lecture notes prepared in connection with the Summer Institute on Axiomatic Set Theory, UCLA, Los Angeles, July 10 — August 4, 1967. 
  13. Frederic Benton Fitch [13] Symbolic Logic, An Introduction, The Ronald Press Co., New York, 1952. Zbl0049.00504
  14. Frederic Benton Fitch [14] "A complete and consistent modal set theory", Journal of Symbolic Logic, Vol. 32 (1967) 93-103. Zbl0158.01202MR237303
  15. P.C. Gilmore [15] "On the epsilon relation", Abstract of paper presented to the Association for Symbolic Logic, Vol. 21 (1956) 219. 
  16. P.C. Gilmore [16] "The monadic theory of types in the lower predicate calculus", Proceedings of the Summer Institute for Symbolic Logic, Cornell University (1957) 309-312. Zbl0178.31001
  17. P.C. Gilmore [17] "An alternative to set theory", American Mathematical Monthly, Vol. 67 (1960) 621-632. MR124201
  18. P.C. Gilmore [18] "Partial set theory", lecture notes prepared in connection with the Summer Institute on Axiomatic Set Theory, UCLA, Los Angeles, July 10 — August 4, 1967. 
  19. P.C. Gilmore [19] "The consistency of partial set theory without extensionality" , IBM Research Report RC1973, Dec. 21, 1967. Zbl0309.02065MR360271
  20. P.C. Gilmore [20] "A theory of identity for partial set theory", a forthcoming manuscript. 
  21. S.C. Kleene [21] Introduction to Metamathematics, Nort-Holland, Amsterdam, 1952. Zbl0047.00703MR51790
  22. Dag Prawitz [22] Natural Deduction, a Proof-Theoretical Study, Almquist and Wiksell, Stockholm, 1965. Zbl0173.00205MR193005
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  26. Solomon Feferman and G. Kreisel [26] "Persistent and invariant formulas relative to theories of higher order", Bulletin of the American Mathematical Society, Vol. 72 (1966) 480-485. Zbl0234.02038MR193007
  27. A. Heyting [27] Intuitionism, an Introduction, North-Holland Publishing Co., Amsterdam, 1946. Zbl0070.00801MR75147
  28. H. Weyl [28] Das Koninuum. Kritische Untersuchungen über die Grundlagen der Analysis, Leipzig, 1918. JFM46.0286.01
  29. Rodger C. Lyndon [29] "Properties preserved under homomorphism", Pacific Journal of Mathematics, Vol. 9 (1959) 143-154. Zbl0093.01101MR108441

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