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The second-order logic without these restrictions is sometimes called full second-order logic to distinguish it from the monadic version. Monadic second-order logic is particularly used in the context of Courcelle's theorem, an algorithmic meta-theorem in graph theory. The MSO theory of the complete infinite binary tree is decidable.
The monadic second-order theory of the infinite complete binary tree, called S2S, is decidable. [8] As a consequence of this result, the following theories are decidable: The monadic second-order theory of trees. The monadic second-order theory of under successor (S1S). WS2S and WS1S, which restrict quantification to finite subsets (weak ...
A subsystem of second-order arithmetic is a theory in the language of second-order arithmetic each axiom of which is a theorem of full second-order arithmetic (Z 2). Such subsystems are essential to reverse mathematics , a research program investigating how much of classical mathematics can be derived in certain weak subsystems of varying strength.
Second-order theories understand existence as a second-order property rather than a first-order property. They are often seen as the orthodox position in ontology. [77] For instance, the Empire State Building is an individual object and "being 443.2 meters (1,454 ft) tall" is a first-order property of it. "Being instantiated" is a property of ...
Simulacra and Simulation (French: Simulacres et Simulation) is a 1981 philosophical treatise by the philosopher and cultural theorist Jean Baudrillard, in which he seeks to examine the relationships between reality, symbols, and society, in particular the significations and symbolism of culture and media involved in constructing an understanding of shared existence.
The existence theory for elliptic operators, using Gårding's inequality, Lax–Milgram lemma and Fredholm alternative, states the sufficient condition for a weak solution u to exist in the Sobolev space H k. For example, for a Second-order Elliptic operator as in Example 2,
The disjunction property is satisfied by a theory if, whenever a sentence A ∨ B is a theorem, then either A is a theorem, or B is a theorem.; The existence property or witness property is satisfied by a theory if, whenever a sentence (∃x)A(x) is a theorem, where A(x) has no other free variables, then there is some term t such that the theory proves A(t).
The pseudo Jahn–Teller effect (PJTE), occasionally also known as second-order JTE, is a direct extension of the Jahn–Teller effect (JTE) where spontaneous symmetry breaking in polyatomic systems (molecules and solids) occurs even when the relevant electronic states are not degenerate. The PJTE can occur under the influence of sufficiently ...