Mereological sets of distributive classes

Andrzej Pietruszczak



We will present an elementary theory in which we can speak of mereological sets composed of distributive classes. Besides the concept of a distributive class and the membership relation, it will possess the notion of a mereological set and the relation of being a mereological part. In this theory we will interpret Morse’s elementary set theory (cf. Morse [11]). We will show that our theory has a model, if only Morse’s theory has one.

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D. van Dalen, Logic and Structure, Third Edition, Berlin 1994.

A. Dold, Lectures on Algebraic Topology, Berlin – Heidelberg – New York 1972.

W. Guzicki, P. Zbierski, Podstawy teorii mnogości, Warszawa 1978.

T. J. Jech, Lectures in Set Theory with Particular Emphasis on the Method of Forsing, Berlin – Heidelberg – New York 1971.

T. Kotarbiński, Gnosiology. The Scientific Approach to the Theory of Knowledge, Oxford – Wrocław, 1966.

H. S. Leonard, N. Goodman, “The calculus of individuals and its uses”, Journal of Symbolic Logic, 5 (1940), 45–55.

S. Leśniewski, “On the Foundations of Mathematics”, [in:] Collected Works, S. J Surma, J. T. Srzednicki, D. I Barnett and V. F. Rickey (eds.), 174– 382, Dorrdrecht – Boston – London 1992.

D. Lewis, Parts of Classes, Cambridge Mass. 1991.

M. Libardi, Teorie delle parti e dell’intero. Mereolologie estensionali, Quaderni, II 1990, 1–3.

E. Mendelson, Mathematical Logic, Princeton 1964.

A. Morse, A theory of Sets, New York 1965.

A. Nowaczyk, Logiczne podstawy nauk ścisłych, Warszawa 1985.

W. V. O. Quine, From a Logical Point of View, Cambridge Mas. 1964.

Z. Semadeni, A. Wiweger, Wstęp do teorii kategorii i funktorow, wyd. II, Warszawa 1978.

J. R. Shoenfield, Mathematical Logic, Reading, Mass. 1967.

J. Słupecki, L. Borkowski, Elements of Mathematical Logic and Set Theory, Oxford – Warsaw 1967.

P. M. Simons, Parts. A Study in Ontology, Oxford 1987.

A. Tarski, “Foudations of the Geometry of Solids”, [in:] Logic, Semantics, Metamathematics. Papers from 1923 to 1938, 24–29, Oxford 1956.

A. Tarski, “Appendice E”, [in:] J. H. Woodger, The Axiomatic Method in Biology, 161–172, Cambridge 1937.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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