Aspects of categorical algebra in initialstructure categories
... pullback stripping functors, which Wyler calls Top-functors, reflect almost all categorical properties from the base category L to the initial structure category K briefly called INS-category [1,4,5,6,8,11,12,13, 13,16,18,19,20,21,22,37]. So for instance if L is complete, cocomplete, wellpowered, co ...
... pullback stripping functors, which Wyler calls Top-functors, reflect almost all categorical properties from the base category L to the initial structure category K briefly called INS-category [1,4,5,6,8,11,12,13, 13,16,18,19,20,21,22,37]. So for instance if L is complete, cocomplete, wellpowered, co ...
Algebraic Proof Complexity: Progress, Frontiers and Challenges
... Pitassi [Pitassi, 1997] for Nullstellensatz written as algebraic circuits, and was investigated further in [Grigoriev and Hirsch, 2003, Raz and Tzameret, 2008b, Raz and Tzameret, 2008a, Tzameret, 2011] in the context of the polynomial calculus proof system. Recently, Grochow and Pitassi [Grochow and ...
... Pitassi [Pitassi, 1997] for Nullstellensatz written as algebraic circuits, and was investigated further in [Grigoriev and Hirsch, 2003, Raz and Tzameret, 2008b, Raz and Tzameret, 2008a, Tzameret, 2011] in the context of the polynomial calculus proof system. Recently, Grochow and Pitassi [Grochow and ...
Examples - Stacks Project
... was taken from an unpublished note of Bart de Smit and Hendrik Lenstra. See also [Bou61, Exercise III.2.12] and [Yek11, Example 1.8] Let k be a field, R = k[x1 , x2 , x3 , . . .], and m = (x1 , x2 , x3 , . . .). We will think of an element f of R∧ as a (possibly) infinite sum X f= aI xI (using multi ...
... was taken from an unpublished note of Bart de Smit and Hendrik Lenstra. See also [Bou61, Exercise III.2.12] and [Yek11, Example 1.8] Let k be a field, R = k[x1 , x2 , x3 , . . .], and m = (x1 , x2 , x3 , . . .). We will think of an element f of R∧ as a (possibly) infinite sum X f= aI xI (using multi ...
THE LOGIC OF QUANTIFIED STATEMENTS
... • e.g., For some integer x, x is divisible by 5 • e.g., For all integer x, x is divisible by 5 • e.g., there exists two integer x, such that x is divisible by 5. • All above three are now propositions (i.e., they have truth values) ...
... • e.g., For some integer x, x is divisible by 5 • e.g., For all integer x, x is divisible by 5 • e.g., there exists two integer x, such that x is divisible by 5. • All above three are now propositions (i.e., they have truth values) ...
Cut-elimination for provability logics and some results in display logic
... deductive reasoning that is employed in practice. In order to study the properties of this system, Gentzen then constructed yet another proof-system called the sequent calculus. Gentzen’s Hauptsatz or main theorem for the sequent calculus is the cut-elimination theorem which shows how to obtain a st ...
... deductive reasoning that is employed in practice. In order to study the properties of this system, Gentzen then constructed yet another proof-system called the sequent calculus. Gentzen’s Hauptsatz or main theorem for the sequent calculus is the cut-elimination theorem which shows how to obtain a st ...
