[FOM] First Order Logic

Stephen G Simpson simpson at math.psu.edu
Mon Sep 2 12:19:14 EDT 2013

Possibly relevant to this discussion is our recent paper

     Stephen G. Simpson and Keita Yokoyama, Reverse mathematics and
     Peano categoricity, Annals of Pure and Applied Logic, 164, 2013,
     pp. 284-293.  http://dx.doi.org/10.1016/j.apal.2012.10.014.
Carl Hewitt writes:
 > Date: Fri, 30 Aug 2013 17:28:29 -0400
 >    I am having trouble understanding why the proponents of first-order
 >    logic think that second-order systems are unusable.
 >    [Dedekind 1888] and [Peano 1889] thought they had achieved success
 >    because they had presented axioms for natural numbers and real numbers
 >    such that models of these axioms are unique up to isomorphism with a
 >    unique isomorphism.  And later generations of mathematicians were happy
 >    to use these axioms.
 >    [....]

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