Lindenbaum algebras of intuitionistic theories and free categories

Annals of Pure and Applied Logic 35 (C):167-172 (1987)
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Abstract

We consider formal theories synonymous with various free categories . Their Lindenbaum algebras may be described as the lattices of subobjects of a terminator. These theories have intuitionistic logic. We show that the Lindenbaum algebras of second order and higher order arithmetic , and set theory are not isomorphic to the Lindenbaum algebras of first order theories such as arithmetic . We also show that there are only five kernels of representations of the free Heyting algebra on one generator in these Lindenbaum algebras

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Citations of this work

Category theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.
Independent axiomatizability of sets of sentences.Piotr Wojtylak - 1989 - Annals of Pure and Applied Logic 44 (3):259-299.

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