Maximal logics

Author:
Joseph Sgro

Journal:
Proc. Amer. Math. Soc. **63** (1977), 291-298

MSC:
Primary 02H10

MathSciNet review:
0491143

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we present a general method for producing logics on various classes of models which are maximal with respect to a Łoś ultraproducts theorem. As a corollary we show that is maximal. We also show that these maximal logics satisfy the Souslin-Kleene property.

**[B-l]**K. Jon Barwise,*Axioms for abstract model theory*, Ann. Math. Logic**7**(1974), 221–265. MR**0376337****[B-2]**Jon Barwise,*Back and forth through infinitary logic*, Studies in model theory, Math. Assoc. Amer., Buffalo, N.Y., 1973, pp. 5–34. MAA Studies in Math., Vol. 8. MR**0342370****[Be]**Miroslav Benda,*On reduced products and filters*, Ann. Math. Logic**4**(1972), 1–29. MR**0292656****[C-K]**C. C. Chang and H. J. Keisler,*Model theory*, North-Holland, Amsterdam, 1973.**[C-N]**W. W. Comfort and S. Negrepontis,*The theory of ultrafilters*, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 211. MR**0396267****[G-1]**S. Garavaglia,*Completeness for topological languages*, Notices Amer. Math. Soc.**22**(1975), A-473. Abstract #75T-E36.**[G-2]**-,*Model theory of topological structures*, Doctoral Dissertation, Yale Univ., New Haven, Ct., 1976.**[K]**H. J. Keisler,*Formulas with linearly ordered quantifiers. The syntax and semantics of infinitary languages*, Springer-Verlag, Berlin and New York, 1969.**[J]**Finn V. Jensen,*Interpolation and definability in abstract logics*, Synthese**27**(1974), 251–257. On the foundations of mathematics (Colloq., Second Finnish Summer School in Math. Logic, Helsinki, 1973). MR**0505413****[L]**Per Lindström,*On extensions of elementary logic*, Theoria**35**(1969), 1–11. MR**0244013****[McK]**T. A. McKee,*Infinitary logic and topological homeomorphisms*, Z. Math. Logik Grundlagen Math.**21**(1975), no. 5, 405–408. MR**0386996****[S-1]**Joseph Sgro,*Completeness theorems for topological models*, Ann. Math. Logic**11**(1977), no. 2, 173–193. MR**0462913****[S-2]**Joseph Sgro,*Completeness theorems for continuous functions and product topologies*, Israel J. Math.**25**(1976), no. 3-4, 249–272. MR**0539984****[S-3]**-,*The decision problem for*,*the interior operator logic*(in preparation).

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
02H10

Retrieve articles in all journals with MSC: 02H10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0491143-2

Article copyright:
© Copyright 1977
American Mathematical Society