The lattices of numerations of theories containing Peano's arithmetic
The Lebesgue Monotone Convergence Theorem
In this article we prove the Monotone Convergence Theorem [16].MML identifier: MESFUNC9, version: 7.8.10 4.100.1011
The life and work of Bohuslav Balcar (1943--2017)
The limit behaviour of exponential terms
The limit lemma in fragments of arithmetic
The recursion theoretic limit lemma, saying that each function with a graph is a limit of certain function with a graph, is provable in .
The linear refinement number and selection theory
The linear refinement number is the minimal cardinality of a centered family in such that no linearly ordered set in refines this family. The linear excluded middle number is a variation of . We show that these numbers estimate the critical cardinalities of a number of selective covering properties. We compare these numbers to the classical combinatorial cardinal characteristics of the continuum. We prove that = = in all models where the continuum is at most ℵ₂, and that the cofinality of is...
The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space
In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10],...
The logic of categories of partial functions and its applications [Book]
The logic of neural networks.
This paper establishes the equivalence between multilayer feedforward networks and linear combinations of Lukasiewicz propositions. In this sense, multilayer forward networks have a logic interpretation, which should permit to apply logical techniques in the neural networks framework.
The logic of Rumely's local-global principle.
The maximal regular ideal of the semigroup of binary relations
The maximality of the typed lambda calculus and of cartesian closed categories
The Measurability of Complex-Valued Functional Sequences
In this article, we formalized the measurability of complex-valued functional sequences. First, we proved the measurability of the limits of real-valued functional sequences. Next, we defined complex-valued functional sequences dividing real part into imaginary part. Then using the former theorems, we proved the measurability of each part. Lastly, we proved the measurability of the limits of complex-valued functional sequences. We also showed several properties of complex-valued measurable functions....
The measure algebra does not always embed
The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.
The measure extension theorem for subadditive measures in -continuous logics
The measure extension theorem for subadditive probability measures in orthomodular -continuous lattices
The method of averaging and functional differential equations with delay.
The midpoint set of a Cantor set.
The model theory of generalized real closed fields.
The model-completion of Stone algebras