Scrabble?! FINITISTS

Definitions of FINITISTS in various dictionaries:

Finitist set theory (FST) is a collection theory designed for modeling finite nested structures of individuals and a variety of transitive and antitransitive chains of relations between individuals. Unlike classical set theories such as ZFC and KPU, FST is not intended to function as a foundation mathematics, but only as a tool in ontological modeling. FST functions as the logical foundation of the classical layer-cake interpretation, and manages to incorporate a large portion of the functionality of discrete mereology. FST models are of type { U α , S β , ∈ } {\displaystyle \{U_{\alpha },S_{\beta },\in \}} , which is abbreviated as M α , β {\displaystyle {\mathcal {M}}_{\alpha ,\beta }} . U α {\displaystyle U_{\alpha }} is the collection of ur-elements of model M α , β {\displaystyle {\mathcal {M}}_{\alpha ,\beta }} . Ur-elements (urs) are indivisible primitives. By assigning a finite integer such as 2 as the value of α {\displaystyle \alpha } , it is determined that U α {\displaystyle U_{\alpha }} contains exactly 2 urs. S β {\displaystyle S_{\beta }} is a collection whose elements will be called sets. β ≥ 0 {\displaystyle \beta \geq 0} is a finite integer which denotes the maximum rank (nesting level) of sets in S β {\displaystyle S_{\beta }} . Every set in S β {\displaystyle S_{\beta }} has one or more sets or urs or both as members. The assigned α {\displaystyle \alpha } and β {\displaystyle \beta } and the applied axioms fix the contents of U α {\displaystyle U_{\alpha }} and S β {\displaystyle S_{\beta }} . To facilitate the use o...