منابع مشابه
Ramified Frege Arithmetic
Frege’s definitions of zero, predecession, and natural number will be explained below. As for second-order Dedekind-Peano arithmetic, the axiomatization most convenient for our purposes is the following: (1) N0 (2) Nx∧Pxy→ Ny (3) ∀x∀y∀z(Nx∧Pxy∧Pxz→ y = z) (4) ∀x∀y∀z(Nx∧Ny∧Pxz∧Pyz→ x = y) (5) ¬∃x(Nx∧Px0) (6) ∀x(Nx→∃y(Pxy)) (7) ∀F(F0∧∀x∀y(Nx∧Fx∧Pxy→ Fy)→∀x(Nx→ Fx) If (slightly non-standardly) we ...
متن کاملDiscriminants and Ramified Primes
has some ei greater than 1. If every ei equals 1, we say p is unramified in K. Example 1.1. In Z[i], the only prime which ramifies is 2: (2) = (1 + i)2. Example 1.2. Let K = Q(α) where α is a root of f(X) = T 3 − 9T − 6. Then 6 = α3 − 9α = α(α− 3)(α+ 3). For m ∈ Z, α+m has minimal polynomial f(T −m) in Q[T ], so NK/Q(α+m) = −f(−m) = m3 − 9m+ 6 and the principal ideal (α−m) has norm N(α−m) = |m ...
متن کاملImproving comparability between microarray probe signals by thermodynamic intensity correction
Signals from different oligonucleotide probes against the same target show great variation in intensities. However, detection of differences along a sequence e.g. to reveal intron/exon architecture, transcription boundary as well as simple absent/present calls depends on comparisons between different probes. It is therefore of great interest to correct for the variation between probes. Much of ...
متن کاملFinitely Ramified Iterated Extensions
Let p be a prime number, K a number field, and S a finite set of places of K. Let KS be the compositum of all extensions of K (in a fixed algebraic closure K) which are unramified outside S, and put GK,S = Gal(KS/K) for its Galois group. These arithmetic fundamental groups play a very important role in number theory. Algebraic geometry provides the most fruitful known source of information conc...
متن کاملRamified Corecurrence and Logspace
Ramified recurrence over free algebras has been used over the last two decades to provide machineindependent characterizations of major complexity classes. We consider here ramification for the dual setting, referring to coinductive data and corecurrence rather than inductive data and recurrence. Whereas ramified recurrence is related basically to feasible time (PTime) complexity, we show here ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1960
ISSN: 0386-2194
DOI: 10.3792/pja/1195523969