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1-conservativity, -submodels, and the collection schema
 

Summary: Notes on 1
1-conservativity, -submodels, and
the collection schema
Jeremy Avigad
January 8, 2002
Abstract
These are some minor notes and observations related to a paper by
Cholak, Jockusch, and Slaman [3]. In particular, if T1 and T2 are theories
in the language of second-order arithmetic and T2 is 1
1 conservative over
T1, it is not necessarily the case that every countable model of T1 is an
-submodel of a countable model of T2; this answers a question posed
in [3]. On the other hand, for n 1, every countable -model of In
(resp. Bn+1 ) is an -submodel of a countable model of WKL0 + In
(resp. WKL0 + Bn+1 ).
1 1
1-conservativity and -submodels
If T is a theory in the language of second-order arithmetic, a Henkin model M of
T can be viewed as a structure M, SM , . . . , where first-order variables are taken
to range over M, and second-order variables are taken to range over some subset

  

Source: Avigad, Jeremy - Departments of Mathematical Sciences & Philosophy, Carnegie Mellon University

 

Collections: Multidisciplinary Databases and Resources; Mathematics