پديد آورنده :
زماني، نجمه
عنوان :
معرفي يك ارزيابي هنسلي تعريف‌پذير با پيچيدگي سوري بالا
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
صفحه شمار :
شش، [55]ص.: مصور، جدول، نمودار
توصيفگر ها :
ميدان ارزيابي هنسلي , حلقۀ ارزياب , قضيۀ اكس‑كوچن و ارشوف , تعريف پذيري
استاد داور :
عليرضا مفيدي، مجيد سلامت
تاريخ ورود اطلاعات :
1401/07/30
تاريخ ويرايش اطلاعات :
1401/08/23
چكيده فارسي :
در زبان حلقه ها وجود دارد كه 89 و يا يك فرمو ِ ل 98 هدف اين پايان نامه پاسخ دادن به اين سوال است كه آيا يك فرمو ِ ل
تل 1 در مقالۀ [ 11 ] مطرح شده پرس ي هنسلي را بدون پارامتر تعريف كند؟ اين سوال توسط حلقۀ ارزيا ِ ب يك ميدان ارزياب
معرفي مي كنيم كه حلقۀ K = k((Γ1))((Γ است. در پاسخ دادن به اين سوال يك ميدان ارزيابي هنسلي به صورت (( 2
ميدان سري هاي k((Γ بدون پارامتر در زبان حلقه ها تعريف نمي شود. منظور از (( 1 89 و يا 98 ارزياب آن با هيچ فرمول
است. مهم ترين ايده هاي به كار رفته براي پاسخ به اين سوال، محكي از پرستل براي تعريف پذيري Γ هان با گروه ارزياب 1
و همچنين قضيۀ اكس‑كوچن و ارشوف 2 است كه هر دو در پايان نامه آورده 89 و 98 يك حلقۀ ارزياب با فرمول هاي
شده است.
چكيده انگليسي :
The aim of this thesis is to answer the question of whether there is a parameter-free 98- formula or a parameter-free
89- formula that defines the valuation ring of a Henselian valued field in the language of rings. This question has been
raised by Prestel in [11] The aim of this note is to provide a counterexample to Prestel’s question. More precisely, we
show the theorem below:
There are ordered abelian groups Γ1 and Γ2 such that for any PAC field k with k the Henselian valuation
ring Ow = k((Γ1))[Γ2] is ∅ -definable in the field K = k((Γ1))((Γ2)). However, Ow is neither definable by
a ∅ 89 -formula nor by a ∅ -formula in K.
In answering this question, the Henselian valued field K = k((Γ1))((Γ2)) is introduced where its valuation ring is
not defined by any 98- formula or 89- formula without parameters in the language of rings. By k((Γ1)) we mean
the field of Hann series with the valued group Γ1. The main ideas that we rely on are the Characterization Theorem
for definability given by Prestel in [11] and also the and theorem. These two ideas are given in
detail in the thesis. Let Σ be a first order axiom system in the ring language L together with a unary predicate O
and let (K1,O1) j= Σ and (K2,O2) j= Σ. Due to the Characterization Theorem the valuation ring of a Henselian
valued field defines with an 98- formula if and only if
K1 K2 ) O1 O2.
In other words if we get from K1 K2 the conclusion O1 O2 then O can be defined with an 98- formula in
the language of rings. So for that the valuation ring of a Henselian valued field is not defined with an 98- formula
we give an embedding f : K K such that f(O) ⊈ O. To give this embedding we use the Ax and
theorem.
Let be a Henselian valued field with value group Γw and residue field kw. Let
(L, u, Γu, k) be an extension of valued fields. If the value group Γw and residue field kw respectively are existentially
closed in the value group Γu and residue field in the language of ordered group and in the of rings
، then valuation field is existentially closed in (L, u, Γu, ).
In this thesis we consider two embedding for value group and identity embedding for reside field.
استاد داور :
عليرضا مفيدي، مجيد سلامت
