The neat embedding problem and the number of variables required in proofs
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- by Roger D. Maddux PDF
- Proc. Amer. Math. Soc. 112 (1991), 195-202 Request permission
Abstract:
By constructing special relation algebras we show that if $3 < \alpha < \omega$, then \[ {\mathbf {S}}N{{\text {r}}_3}C{A_\alpha } \ne {\mathbf {S}}N{{\text {r}}_3}C{A_{3\alpha - 7}}\] and there is a logically valid first-order sentence containing at most three variables with a proof in which every sentence has at most $3\alpha - 7$ variables, but no proof in which every sentence has at most a variables.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 195-202
- MSC: Primary 03G15; Secondary 03B10, 03F07
- DOI: https://doi.org/10.1090/S0002-9939-1991-1033959-7
- MathSciNet review: 1033959