论文标题
可计数的严格反向数学
Countable strict reverse mathematics
论文作者
论文摘要
我们研究子系统$ com_ {fcn} $，$ comi_ {fcn} $和$ pra_ {fcn} $ function $ etf $的基础理论，是可计数的严格反向数学的基础理论。我们表明，对一元，二进制和三元函数的任何变量的归纳是$ com_ {fcn} $的成对等效的。我们证明，削弱的原始递归axiom $ wpra $等效于$ comi_ {fcn} $上的原始递归axiom $ pra $。我们表明，置换公理和最小值公理$ min^1 $，$ min^2 $，$ min^3 $是$ pra_ {fcn} $的成对等效物。因此，我们介绍了$ ETF $的几种等效公理。
We investigate subsystems $COM_{fcn}$, $COMI_{fcn}$ and $PRA_{fcn}$ of the elementary theory of functions $ETF$, the base theory for countable strict reverse mathematics. We show that inductions on any variable for unary, binary and ternary functions are pairwise equivalent over $COM_{fcn}$. We prove that weakened primitive recursion axiom $WPRA$ is equivalent to primitive recursion axiom $PRA$ over $COMI_{fcn}$. We show that permutation axiom and minimization axioms $MIN^1$, $MIN^2$, $MIN^3$ are pairwise equivalent over $PRA_{fcn}$. Thus, we present several equivalent axiomatizations of $ETF$.
