Ⅰ. INTRODUCTIONLet ◇ denote the diamond principle, □ the box principle, ST_k a Suslin_k-tree. The report presents a new thorough relation between the above combinatorial principles and the Suslin_k-trees.
In [1], Solovay first supposed that ZF+DA_R is consistent, and then he proved the independence of DC from AD by using inner models for AD_R. In this note, we further investigate the relation between the generalized ve...In [1], Solovay first supposed that ZF+DA_R is consistent, and then he proved the independence of DC from AD by using inner models for AD_R. In this note, we further investigate the relation between the generalized version of the principle of dependent choices and the axiom of determinateness. We know that AD implies AC and AC is equivalent展开更多
文摘Ⅰ. INTRODUCTIONLet ◇ denote the diamond principle, □ the box principle, ST_k a Suslin_k-tree. The report presents a new thorough relation between the above combinatorial principles and the Suslin_k-trees.
文摘In [1], Solovay first supposed that ZF+DA_R is consistent, and then he proved the independence of DC from AD by using inner models for AD_R. In this note, we further investigate the relation between the generalized version of the principle of dependent choices and the axiom of determinateness. We know that AD implies AC and AC is equivalent
