Direct Proofs of Lindenbaum Conditionals

Logica Universalis 8 (3-4):321-343 (2014)
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Abstract

We discuss the problem raised by Miller to re-prove the well-known equivalences of some Lindenbaum theorems for deductive systems without an application of the Axiom of Choice. We present five special constructions of deductive systems, each of them providing some partial solutions to the mathematical problem. We conclude with a short discussion of the underlying philosophical problem of deciding, whether a given proof satisfies our demand that the Axiom of Choice is not applied

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10.1007/s11787-013-0081-1

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Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Set theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
What is a Proof?Reinhard Kahle - 2015 - Axiomathes 25 (1):79-91.

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