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Jun
12
awarded  Yearling
May
26
comment first order logic models
The answer will (obviously) be 'no'. To see this, suppose $\varphi$ were such a sentence and either induct on complexity or put it in some sort of normal form ('prenex normal form' seems to be the phrase used on Wikipedia). The analysis may be tedious, but should come with relative ease.
Jan
5
comment Must vectors in $\mathbb{R}^n$ have their “tail” at origin?
When you think of $\mathbb{R}^n$ geometrically as a vector space, you are considering each vector as a direction arrow with a tail at the origin. So $(0, 10) - (0, 9)$ is an arrow $(0, 1)$ with a tail at the origin. Vectors here are only directions; the arrow you would want to draw from the head of one vector to the head of the other is not actually a vector unless you translate it back to the origin. If you try to define a vector space structure on $\mathbb{R}^n$ using the geometric interpretation of addition above, you'll run into problems (e.g. with additive identity).
Nov
21
answered is it possible for two fields with the same characteristic to not be isomorphic?
Nov
13
answered A subgroup $H$ is normal in $G$ if and only if…
Nov
6
revised Evaluate the limit without L'Hospital
fixed texing
Nov
6
suggested suggested edit on Evaluate the limit without L'Hospital
Oct
28
comment What is $R(\omega)$ (and where can I find definitions for similar common notation)?
Most books have an index of symbols at the back (my copy of Chang & Keisler does), which you can use to find where things are first defined. $R(\omega)$ is defined inductively on p. 45, and more clearly on p. 588.
Oct
28
revised $\omega$-categoricity of a theory
added 76 characters in body
Oct
28
answered $\omega$-categoricity of a theory
Oct
27
suggested suggested edit on Why $p \leftrightarrow q$ is equivalent to $(p \wedge q) \vee (\neg p \wedge \neg q)$? Without using the truth table
Oct
27
revised Is every theorem of PA true in the standard model of number theory $N$?
added 81 characters in body
Oct
27
revised Is every theorem of PA true in the standard model of number theory $N$?
added 674 characters in body
Oct
27
revised Is every theorem of PA true in the standard model of number theory $N$?
added 674 characters in body
Oct
27
answered Is every theorem of PA true in the standard model of number theory $N$?
Oct
26
answered Limit of function (definition)
Oct
26
awarded  Commentator
Oct
26
comment Definition of Vector Space
Sorry, I might've been a little over-enthusiastic. Fixed!
Oct
26
answered Definition of Vector Space
Oct
26
answered what is the meaning of a symbol $\pi_1(X,x_0)=0$