Premium
Some More Conservation Results on the Baire Category Theorem
Author(s) -
Yamazaki Takeshi
Publication year - 2000
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/(sici)1521-3870(200001)46:1<105::aid-malq105>3.0.co;2-2
Subject(s) - mathematics , baire category theorem , arithmetic function , baire measure , baire space , set (abstract data type) , pure mathematics , discrete mathematics , computer science , programming language
In this paper, we generalize a result of Brown and Simpson [1] to prove that RCA 0 +Π 0 ∞ ‐BCT is conservative over RCA 0 with respect to the set of formulae in the form ∃! X φ ( X ), where φ is arithmetical. We also consider the conservation of Π 0 0∞ ‐BCT over Σ b 1 ‐NIA+∇ b 1 ‐CA.