ON THE ROLE OF THE COLLECTION PRINCIPLE FOR Σ2-FORMULAS IN SECOND-ORDER REVERSE MATHEMATICS
ON THE ROLE OF THE COLLECTION PRINCIPLE FOR Σ2-FORMULAS IN SECOND-ORDER REVERSE MATHEMATICS
复制标题
论Σ2-公式的集合原理在二阶逆数学中的作用
DOI：
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发表时间：
2009
期刊：
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通讯作者：
Yue Yang
中科院分区：
文献类型：
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作者：
C. Chong;S. Lempp;Yue Yang
我们表明，从Hirschfeldt和海岸的原则部分是等价的，在RCA 0的B2-Bounding原则B B 0 2，回答他们的一个开放的问题。此外，我们还填补了一个空白的证明Cholak，Jockusch和Slaman表明，D2 2意味着B 0 2，因此确实相当于稳定拉姆齐定理对（SRT 2）。这也使我们能够得出结论，Dzhafarov和Hirst定义的组合原则IPT 2，SPT 2 2和SIPT 2 2都隐含B 2，因此SPT 2 2和SIPT 2 2也都等价于SRT 2 2。我们的证明使用的概念，一个双驯服削减，我们证明的存在是等价的，在RCA 0，失败的B 2。
We show that the principle PART from Hirschfeldt and Shore is equivalent to the Σ2-Bounding principle BΣ 0 2 over RCA0, answering one of their open questions. Furthermore, we also fill a gap in a proof of Cholak, Jockusch and Slaman by showing that D2 2 implies BΣ 0 2 and is thus indeed equivalent to Stable Ramsey’s Theorem for Pairs (SRT2). This also allows us to conclude that the combinatorial principles IPT2, SPT 2 2 and SIPT 2 2 defined by Dzhafarov and Hirst all imply BΣ2 and thus that SPT 2 2 and SIPT 2 2 are both equivalent to SRT 2 2 as well. Our proof uses the notion of a bi-tame cut, the existence of which we show to be equivalent, over RCA0, to the failure of BΣ2.