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You can leave a response , or trackback from your own site. I like that argument that 7 may be nonstandard, since it takes 7 symbols to write a proof that 7 exists, and that's too long to be acceptable, since every nonstandard number n has a proof of length n that it exists.

"On automorphisms of models of Peano arithmetic" by Ermek S Nurkhaidarov

Yeah, I know, that took 7 symbols, but this isn't some circular argument that 7 exists because that proof exists because 7 exists; 7 exists because the proof exists because it's right there in front of me! It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired….


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Einstein, simply because he had more endurance. You might get that from Lowenheim-Skolem theorem. Even Nelson tried to prove Peano arithmetic was inconsistant as have a few other mathematical logicians.


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  6. See Part 9 of the series in diagonalargument. You are commenting using your WordPress.

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    ISBN 13: 9780198532132

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    Models of Peano Arithmetic

    RSS - Posts. RSS - Comments. Enter your email address to subscribe to this blog and receive notifications of new posts by email. Sign me up! This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic.

    Addition (Peano definition)

    Major representation theorems are proved, and the important particular case of countable recursively saturated models is discussed in detail. All necessary technical tools are developed.

    Bestselling Series

    The list includes: constructions of elementary simple extensions; a partial classification of arithmetic types, in particular Gaifman's theory of definable types; forcing in arithmetic; elements of the Kirby-Paris combinatorial theory of cuts; Lascar's gener The list includes: constructions of elementary simple extensions; a partial classification of arithmetic types, in particular Gaifman's theory of definable types; forcing in arithmetic; elements of the Kirby-Paris combinatorial theory of cuts; Lascar's generic automorphisms; and applications of Abramson and Harrington's generalization of Ramsey's theorem.

    Keywords: nonstandard models , countable recursively saturated models , Gaifman's theory , Kirby-Paris , Lascar's generic automorphisms , Ramsey's theorem. Forgot password? Don't have an account? All Rights Reserved.

    Nonstandard Models of Arithmetic

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