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counting, ordering, matching, combining, separating, and locating in space and time, and the idea that these processes are abstract and the idea that they are endlessly repeatable order, succession, collection, relation, rule and operation property the logical particles
(N+, 1, Sc, <) "Certain facts about this structure are evident (if we formulate them at all): < is a total ordering, 1 is the least element, and m < n implies Sc(m) < Sc(n)." the least number principle for the positive integers (N+, 1, Sc, <, +, ×) , where + is concatenation of tallies, and * is repetition of + induction successor_a "where a is an element of an index collection A. We may conceive of the objects of the resulting structure as words on the alphabet A”, with Sc (w) = wa in the sense of concatenation. Of special interest ... is the case that A = {0, 1}, for which we also conceive of the words on A as the finite paths in the binary branching tree, alternatively as the end nodes of such paths. integers rationals commutativity, associativity, distributivity, and cancellation divisibility, isPrime, mod
-- http://logic.harvard.edu/EFI_Feferman_IsCHdefinite.pdf (or http://math.stanford.edu/~feferman/papers/Conceptual_Structuralism.pdf , but i recommend the paper over the slides)
homogeneous hypergraph
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relations hypergraphs chu spaces algebras homomorphisms points sets (and power set operation?) topologies categories nodes, edges, paths natural numbers terms grammars ordered sequences/lists/tuples functions logical propositions/sentences inference rules/reductions proofs boolean values posets lattices types hypercategory? [my own idea; a hypergraph with optional equalivalences over paths, semi-equivalently a composition operation over paths] topoi [topos's] variables and substitution/anti-substitution [my term for tdn lambda calculus's 'abstraction' operation] e.g. the lambda calculus induction trees formal languges automata groups cardinal ordinal computation http://homotopytypetheory.org/book/
some random models of computation: memory-to-memory machines (ram machine; no registers) stack machine (no registers) register machine combinatorial calculus lambda calculus turing machine accumulator machine which have only one visible general-purpose temp register
note to self: look at l/say.txt, there might be something on that list that isnt here
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papers on various approaches:
