Open Access
2011 Reverse Mathematics and Uniformity in Proofs without Excluded Middle
Jeffry L. Hirst, Carl Mummert
Notre Dame J. Formal Logic 52(2): 149-162 (2011). DOI: 10.1215/00294527-1306163


We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$ sentence of a certain form is provable using E-HA${}^\omega$ along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the Dialectica interpretation. These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical principles in subsystems of constructive analysis.


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Jeffry L. Hirst. Carl Mummert. "Reverse Mathematics and Uniformity in Proofs without Excluded Middle." Notre Dame J. Formal Logic 52 (2) 149 - 162, 2011.


Published: 2011
First available in Project Euclid: 28 April 2011

zbMATH: 1225.03083
MathSciNet: MR2794648
Digital Object Identifier: 10.1215/00294527-1306163

Primary: 03F35 , 03F50
Secondary: 03B30 , 03F60

Keywords: Dialectica , proof theory , realizability , reverse mathematics , uniformization

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 2 • 2011
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