Every BA is isomorphic to a Lindenbaum-Tarski algebra.
This application is called Simorgh, an open source, isomorphic single page application developed by the World Service languages team.
These are pairs of functors between two categories 𝒜 and ℬ, which go in opposite directions such that a one-to-one correspondence exists between the set of arrows F(A) → B in ℬ and the set of arrows A → G(B) in 𝒜—that is, such that the sets are isomorphic.
If there is no ether, a model can’t be isomorphic to it.
Are there any other models, that is, models not isomorphic to R.
We say that two structures are isomorphic if there is an isomorphism from one to the other.
First, as indicated above, sentences in logical languages do not distinguish isomorphic models.
., Došen 1997, 2006), formulas such as A ∧ B and A ∧ (A → B) are equivalent, but not isomorphic.
In other words two structures are topos isomorphic if their canonical representatives are isomorphic in the internal language of some topos.
As a consequence, Benacerraf’s dilemma of isomorphic numbers systems with different set-theoretic properties does not arise in the context of categorical set theory.
Given Putnam's conclusion, any physical system with inputs and outputs isomorphic to i and o implements all of the infinitely many automata with input i and output o.
Most immediately, to understand Aristotle’s approach to thinking, it is necessary to determine what it means to say that a thinker’s mind and its object become isomorphic.
This joke reminds us that the theory of natural numbers, so central to Frege’s works, appears in PM as only a special case of a general theory of cardinal and ordinal numbers and even more general classes of isomorphic structures.
Thus, one could say that things in the world are isomorphic with concepts, and that concepts in turn are isomorphic with words insofar as our use of language follows the way we think and this in turn follows the way the world is.
While none of these two notions is the one we have in ranking theory, Spohn (2009), relying on Halpern (2003), shows that by adopting the second notion of conditional possibility one can render possibility theory isomorphic to a real-valued version of ranking theory.
In other words, the pure counterfactual account requires the mapping between computational and physical descriptions to be such that the counterfactual relations between the physical states are isomorphic to the counterfactual relations between the computational states.
Important special classes of mappings are homomorphisms in algebra, isometries in geometry, operators in analysis, homeomorphisms in topology, representations in group theory, and isomorphisms in a variety of contexts (see foundations of mathematics: Isomorphic structures).
In his letter to DeWitt, Everett described how he understood the aim of physical inquiry: “There can be no question of which theory is ‘true’ or ‘real’ — the best that one can do is reject those theories which are not isomorphic to sense experience” (Barrett and Byrne 2012, 253).
We say that two similar structures A, B are Boolean isomorphic, written A ≅b B, if, for some complete Boolean algebra B, we have V(B) ⊨ A ≅ B, that is, if there is a Boolean extension of the universe of sets in which the canonical representatives of A and B are isomorphic with Boolean value 1.
On the counterfactual supposition of a shift in wind, what results is a redness exactly like the actual one, which is in perfectly isomorphic resemblance relations to its worldmates as the actual one is to its worldmates, with just a slight difference in distance with respect to, e.g., the roundness of the moon.
isomorphic
adj pert
- having similar appearance but genetically different
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On the counterfactual supposition of a shift in wind what results is a redness exactly like the actual one which is in perfectly isomorphic resemblance relations to its worldmates as the actual one is to its worldmates with just a slight difference in distance with respect to eg the roundness of the moon