麻豆传媒视频网站

Here is a template for introducing mathematical objects: 鈥淥bjects are found in stages. For every stage S: (1) for any things found before S, you find at S the bland set whose members are exactly those things; (2) for anything, x, which was found before S, you find at S the result of tapping x with any magic wand (provided that the result is not itself a bland set); you find nothing else at S.鈥�

This Template has rich applications, it realizes John Conway鈥檚 (1976) Mathematicians鈥� Liberation Movement, and it generalizes a lovely idea due to Alonzo Church (1974). Some parts of this Template are familiar: the bit about bland sets is just the ordinary story we tell about the cumulative iterative conception of set. But this talk of 鈥渕agic wands鈥� is new and different. Moreover, parts of the Template are left unspecified.

This under-specification is deliberate: we want to be able to flesh out the Template in umpteen different ways. The Main Theorem of the paper is that any loosely constructive way of fleshing out the Template is synonymous with a ZF-like theory.