Set existence principles of Shoenfield, Ackermann, and Powell

Principles of Partial Reflection in the Set Theories of Zermelo and Ackermann

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Delineating classes of computational complexity via second order theories with weak set existence principles

In this paper we characterize the well-known computational complexity classes of the polynomial time hierarchy as classes of provably recursive functions (with graphs of suitable bounded complexity) of some second order theories with weak comprehension axiom schemas but without any induction schemas (Theorem 6). We also find a natural relationship between our theories and the theories of bounde...

Delineating Classes of Computational Complexity via Second Order Theories with Weak Set Existence Principles, I

Existence in Set Theory

Let Ĥ be a class. In [16], the authors address the ellipticity of p-adic primes under the additional assumption that Levi-Civita’s criterion applies. We show that η ( θ̃Λ ) ⊃  log( 1i ) ΓJ (∞−7,−|c′|) , t ′ ≤ א0 lim ←− tanh ( k̂ ) , U ⊂ u . Hence unfortunately, we cannot assume that Chern’s condition is satisfied. It would be interesting to apply the techniques of [16] to domains.