ABSTRACT
Starting with infinite language categories (Nourani, 1995), and Chapter 3, specific techniques for creating functorial models based on fragments are presented in this chapter.
The model bases are Fragment Consistency Models where new techniques for creating generic models are defi ned. Infi nitary positive language categories are defi ned and infi nitary complements to Robinson consistency from the author’s preceding papers are further developed to present new positive omitting types techniques and infi nitary positive fragment higher stratifi ed computing categories. Further neoclassic model-theoretic consequences are presented in (Nourani, 2005a). Positive categories and Horn categories are new fragment categories defi ned and the applications to a Positive Process algebraic computing (Nourani, 2005) is briefed on algebraic topology and computing (Nourani, 2011). For example, the author defi ned the category LP, ω to be the category with objects positive fragments and arrows the subformula preorder on formulas to present models. Start with a well-behaved countable fragment of an infi nitary language L ω1, w from Chapter 3. Let L ω1, K be the least fragment of L ω1, w that contains L<A>. Each formula j in K<A> contains only fi nitely many c in C. This implies when raking leaves on the trees, there are only fi nite number of named branches claimed by constant names. However, the infi nite trees are defi ned by function names. The functions defi ne the model with the constants. From the functorial view what follows resembles to a cosmic scooping from fragments the model theoretic specifi cs for a functorial model theory.
