A conservation result concerning bounded theories and the collection axiom
A conservation result concerning bounded theories and the collection axiom
We present two proofs, one proof-theoretic and one model-theoretic, showing that adding the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper B normal upper Sigma 1 Superscript 0"> <mml:semantics> <mml:mrow> <mml:mi>B</mml:mi> <mml:msubsup> <mml:mi mathvariant="normal">Σ<!-- Σ --></mml:mi> <mml:mn>1</mml:mn> <mml:mn>0</mml:mn> </mml:msubsup> </mml:mrow> <mml:annotation encoding="application/x-tex">B\Sigma _1^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-collection axioms to any bounded first-order theory <inline-formula …