The neat embedding problem and the number of variables required in proofs

Author:
Roger D. Maddux

Journal:
Proc. Amer. Math. Soc. **112** (1991), 195-202

MSC:
Primary 03G15; Secondary 03B10, 03F07

MathSciNet review:
1033959

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Abstract | References | Similar Articles | Additional Information

Abstract: By constructing special relation algebras we show that if , then

**[HMT71]**Leon Henkin, J. Donald Monk, and Alfred Tarski,*Cylindric algebras. Part I*, Studies in Logic and the Foundations of Mathematics, vol. 64, North-Holland Publishing Co., Amsterdam, 1985. With an introductory chapter: General theory of algebras; Reprint of the 1971 original. MR**781929****[HMT85]**Leon Henkin, J. Donald Monk, and Alfred Tarski,*Cylindric algebras. Part II*, Studies in Logic and the Foundations of Mathematics, vol. 115, North-Holland Publishing Co., Amsterdam, 1985. MR**781930****[J69]**James S. Johnson,*Nonfinitizability of classes of representable polyadic algebras*, J. Symbolic Logic**34**(1969), 344–352. MR**0256862****[Ma78]**Roger D. Maddux,*Topics in relation algebras*, Doctoral dissertation, University of California, Berkeley, 1978, pp. iii+241.**[Ma82]**Roger Maddux,*Some varieties containing relation algebras*, Trans. Amer. Math. Soc.**272**(1982), no. 2, 501–526. MR**662049**, 10.1090/S0002-9947-1982-0662049-7**[Ma85]**Roger Maddux,*Finite integral relation algebras*, Universal algebra and lattice theory (Charleston, S.C., 1984) Lecture Notes in Math., vol. 1149, Springer, Berlin, 1985, pp. 175–197. MR**823016**, 10.1007/BFb0098465**[Ma89]**Roger D. Maddux,*Nonfinite axiomatizability results for cylindric and relation algebras*, J. Symbolic Logic**54**(1989), no. 3, 951–974. MR**1011183**, 10.2307/2274756**[Mo69]**J. Donald Monk,*Nonfinitizability of classes of representable cylindric algebras*, J. Symbolic Logic**34**(1969), 331–343. MR**0256861****[Mo71]**J. Donald Monk,*Provability with finitely many variables*, Proc. Amer. Math. Soc.**27**(1971), 353–358. MR**0276063**, 10.1090/S0002-9939-1971-0276063-5**[TG87]**Alfred Tarski and Steven Givant,*A formalization of set theory without variables*, American Mathematical Society Colloquium Publications, vol. 41, American Mathematical Society, Providence, RI, 1987. MR**920815**

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1033959-7

Article copyright:
© Copyright 1991
American Mathematical Society